In the past, we have substantially increased the resolution and sensitivity of the technique by introducing diffusional deconvolution to the calculation of sedimentation coefficient distributions. This has become the state-of-the-art of sedimentation velocity analytical ultracentrifugation and is widely applied by research laboratories in this field. Computationally, this method required the solution of the Lamm equation (governing the evolution of the spatial macromolecular concentration profile), and the inversion of an integral equation in conjunction with maximum entropy regularization. Recently we have been able to significantly further increase the resolution of the method by replacing maximum entropy regularization step with a more general Bayesian analysis, and by introducing size-and-shape distribution methods. This strategy is also the method of choice for the detection of trace protein oligomeric species, which is a topic of great general interest for the study of assembly nucleation events, and of high importance for the detection of immunogenic aggregates in biotechnology. We have refined the application of Bayesian regularization, to reliably detect protein oligomers below the 1% limit. More recently, on the theoretical side, we have made significant progress in our understanding of co-sedimentation of rapidly reacting systems. This has led to the development of an effective particle model, which has the promise of providing a robust theoretical framework for the analysis of multi-component systems. We have also made great progress in understanding the experimental limitations and increasing the accuracy of sedimentation velocity experiments by accounting for the finite temporal and spatial resolution of the absorbance optical scanner. Further, we have experimentally examined the role of optical aberations due to Wiener skewing, which was suspected in the field to be a significant factor. This was not confirmed for experimental conditions generally in use. With regard to the development of applications, we have continued to explore applications of analytical ultracentrifugation to the characterization of nanoparticles. Further, we have embarked on the study of lipid vesicles as a platform for quantifying protein-protein-membrane interactions.